On Sun, Mar 23, 2008 at 03:37:27AM -0700, Brian Tenneson wrote: > > <begin their argument for the non-existence for the universe> > Definition: To contain means <insert something most people would > accept here>. The notation and word for 'is contained in' is > is<in. > > Thing and exists are undefined or ... acceptably defined only be > common intuitive sense of what a thing is, but neither formally (in > her argument) > > Definition: the universe (call it U) is a thing that has the property > that it contains all things, notated by (x) (x is<in U), where x is a > thing. > > Theorem: If the universe exists then the (three or so) axioms of > binary logic are inconsistent. > Proof: The method is to show that if U exists then there is a logical > statement (ie, a WELL FORMED formula) that is true if and only it is > false, being simultaneously, to abuse language, true and not true, > which violates the +definition+ of the words not and and. > > Suppose U exists. Then apply Russell's approach. Given how broad and > vague 'thing' is defined, let's discuss the thing, call it S, this > thing called S is the thing that contains all things that don't > contain themselves. In the notation, let S be the thing (given the > vagueness of 'thing', S is a thing) such that > (x) (x is<in S if and only if x!<x). > In other words, S is the thing such that for all things x, x is > contained in S if and only if x is not contained in x. > > Since we wrote (x), then apply to S by an application of some > universal quantifier rule, which most people would accept (and maybe > they should qualify the universal sometimes) to S. Then you get, just > as Russell's approach: > > (S is<inS if and only if S!<S). > > This contradiction proves the theorem. That if the universe exists, > then binary logic is inconsistent. > > > Corollary: The universe does not exist. > "Proof:" Binary logic is consistent, therefore, by contraposition of > the theorem, the universe does not exist. > > <end their argument for the non-existence for the universe> > > > I've been banging away at this keyboard for a while so I'll post this > and take a break. > > The idea came to me when I tried basically to prove her argument that > the universe does NOT exist, wrong. It occurred to me that three > truth values are sufficient to make the usual proof by contradiction > +not a tautology+. And, therefore, even in 3-valued logic, her > argument fails. > > Obviously, that doesn't prove the universe does exist, it just proves > her argument that is doesn't is wrong. > > > > > > > > <end their argument for the non-existence for the universe> >

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Maybe it instead proves that "things" like S do not exist in the universe. OK, it means we have to change the definition of universe a bit, but this is not so strange as universe really just means all that exists. So, yeah, I'd say it was a bit of linguistic sophistry, rather than being too profound. Anyway, the question of whether Russell's paradox can be found to not hold force in non-standard logic seems interesting, and potentially well motivated for the MUH case which ab initio would include things like S in the level 4 "multiverse". Cheers ---------------------------------------------------------------------------- A/Prof Russell Standish Phone 0425 253119 (mobile) Mathematics UNSW SYDNEY 2052 [EMAIL PROTECTED] Australia http://www.hpcoders.com.au ---------------------------------------------------------------------------- --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---